1RB1LD_1RC1RB_1LC1LA_0RC0RD

1RB1LD_1RC1RB_1LC1LA_0RC0RD (bbch)

Blanking Beaver BLB(4,2) champion which creates a blank tape after 32,779,477 steps. It was discovered and reported by Nick Drozd in 2021.

Analysis by Shawn Ligocki

Let

$$D(a,b)=0^{\infty }\;1^{a}\;0^{b}\;{\textrm {D>}}\;0^{\infty }$$

then:

$${\begin{array}{lc}D(a+3,&b)&\to &D(a,b+5)\\D(0,&b)&=&{\textrm {Blank}}\\D(1,&b)&\to &D(b+2,4)\\D(2,&b)&\to &D(b+3,4)\\\end{array}}$$

let $D(a)=D(a,4)$, then we can simplify to:

$${\begin{array}{lc}D(3k)&\to &{\textrm {Blank}}\\D(3k+1)&\to &D(5k+6)\\D(3k+2)&\to &D(5k+7)\\\end{array}}$$

Starting from $D(2)$ (at step 19) we get the trajectory:

$${\begin{array}{l}D(2)&\to &D(7)&\to &D(16)&\to &D(31)&\to &D(56)&\to &D(97)\\&\to &D(166)&\to &D(281)&\to &D(472)&\to &D(791)&\to &D(1322)\\&\to &D(2207)&\to &D(3682)&\to &D(6141)&\to &{\textrm {Blank}}\\\end{array}}$$

which has the remarkable luck of applying this Collatz-like map 14 times before reaching the blanking config (expected # of applications before halting is 3).